The UKIRT Infrared Deep Sky Survey is a set of five surveys of complementary combinations of area, depth, and Galactic latitude, which began in 2005 May. The surveys use the UKIRT Wide Field Camera (WFCAM), which has a solid angle of 0.21deg^2. Here we introduce and characterise the ZYJHK photometric system of the camera, which covers the wavelength range 0.83-2.37 microns. We synthesise response functions for the five passbands, and compute colours in the WFCAM, SDSS and 2MASS bands, for brown dwarfs, stars, galaxies and quasars of different types. We provide a recipe for others to compute colours from their own spectra. Calculations are presented in the Vega system, and the computed offsets to the AB system are provided, as well as colour equations between WFCAM filters and the SDSS and 2MASS passbands. We highlight the opportunities presented by the new Y filter at 0.97-1.07 microns for surveys for hypothetical Y dwarfs (brown dwarfs cooler than T), and for quasars of very--high redshift, z>6.4.
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